[16 pts] Solve the following optimization problems: (a) A mining company in northern Alberta needs to transport valuable minerals form a recently created mining facility (Point M ) to the processing plant (point P ). The mine is located 36 km from an existing rail line (point Q ), which is 200 km from the processing plant. You are tasked with building a direct road that connects point M to some part of the train track at point R , a distance of x km from Q; see the diagram in the pdf-file on eClass. Mine operators find that transporting by road costs $10 per km, whereas by rail it costs $8 per km. Find the value of x that minimizes the cost for the company.

(b) A poster needs to be made with the following specifications: The total area of the poster should be 3000 cm2 . It should have 1 cm margin at the bottom, 3 cm margin each at both sides, and 4 cm margin at the top. What dimensions will give the largest printed area?